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The Construction of Logical Space$
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Agustín Rayo

Print publication date: 2013

Print ISBN-13: 9780199662623

Published to Oxford Scholarship Online: September 2013

DOI: 10.1093/acprof:oso/9780199662623.001.0001

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Introducing Mathematical Vocabulary

Introducing Mathematical Vocabulary

Chapter:
(p.180) 8 Introducing Mathematical Vocabulary
Source:
The Construction of Logical Space
Author(s):

Agustín Rayo

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199662623.003.0008

This chapter develops an account of linguistic stipulation from the perspective of the compositionalist: someone who thinks that a language involving object-talk is attractive insofar as it enables us to give a recursive specification of truth-conditions for a class of sentences rich in expressive power, but not because it has some additional virtue. The chapter explains how the compositionalist should think of linguistic stipulation, and suggests sufficient conditions for successful stipulation. The upshot is that all it takes for an axiom system to succeed in introducing a new piece of mathematical vocabulary is that it be internally coherent (in the case of pure mathematics) or conservative (in the case of applied mathematics).

Keywords:   linguistic stipulation, internally coherent axiom system, conservative axiom system, compositionalism, logical consequence, semantics, truth-conditions

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